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High Energy Physics - Theory, hep-th,General Relativity and Quantum Cosmology, gr-qc
Abstract:
We calculate the Kaluza-Klein spectrum of spin-2 fluctuations around the
${\cal N}=3$ warped ${\rm AdS}_4\times M_6$ solution in massive IIA
supergravity. This solution was conjectured to be dual to the $D=3$ ${\cal
N}=3$ superconformal ${\rm SU}(N)$ Chern-Simons matter theory with level $k$
and 2 adjoint chiral multiplets. The ${\rm SO}(3)_R\times{\rm SO}(3)_D$
isometry of the ${\cal N}=3$ solution is identified with the ${\rm
SU}(2)_F\times {\rm SU}(2)_{\cal R}$ global symmetry of the dual ${\cal N}=3$
SCFT. We show that the ${\rm SO}(3)_R\times{\rm SO}(3)_D$ quantum numbers and
the ${\rm AdS}$ energies carried by the BPS spin-2 modes match precisely with
those of the spin-2 gauge invariant operators in the short multiplets of
operators in the ${\cal N}=3$ SCFT. We also compute the Euclidean action of the
${\cal N}=3$ solution and the free energy of the ${\cal N}=3$ SCFT on $S^3$, in
the limit $N\gg k$. Remarkably, the results show a complete agreement.
